The phrase "approval by both" is correct and usable in written English.
It can be used in contexts where a decision or agreement requires consent from two parties.
Example: "The project will proceed only after receiving approval by both the manager and the client."
Alternatives: "consent from both" or "agreement from both parties".
The conference report approved Friday is subject to approval by both chambers of Congress, a process that is expected to begin on Tuesday with action by the House and then by the Senate — where 60 votes will be required to end debate.
The deal is subject to approval by both governments.
The agreement awaits final approval by both houses.
A new governor is subject to approval by both houses of Parliament.
The agreement is subject to approval by both CUNY's trustees and the union membership.
A final treaty will need approval by both German parliaments before it takes effect.
Ethical approval was sought and approved by both the University of California at Berkeley (Approval #: 2011-01-2722) and the Ministry of Health in Cambodia through the Population Council.
The projects would arouse a lengthy discussion and almost certainly require a variety of approvals by both the Pataki administration and the City Council, since the plans involve issuing bonds, leasing park land and spending more than $1.5 billion.
The plan of study should contain the following: i) A cover sheet for approvals by both dissertation advisors, both DGSs, and by the appropriate associate dean of the Graduate School, ii) an introduction where the student explains the rational for proposing the ad hoc combined degree, and iii) a semester by semester time line listing all classes, teaching, and required examinations.
Pfizer's proposed acquisition requires approval by regulators in both the United States and Europe.
The transaction is subject to approval by directors of both concerns and shareholders of Collins.
